
Let \(\mathbf {B}^*\)  be an optimal solution to the above optimization program. Then,
\(\mathbf {B}^*\)  must satisfy the following KKT conditionsAs this optimization
program is not convex, a set of constraint qualifications (CQs) should be
checked to make sure that the KKT conditions indeed hold. The CQs stated in
Appendix IV of [1]} hold in a trivial manner for this program.:
\((\mathbf {B}^*+\mathbf {N}_1)^{-1}+\mu (\mathbf {B}^*+\mathbf {N}_3)^{-1}+\mathbf {M}_1&=(1+\mu )(\mathbf {B}^*+\mathbf {N}_2)^{-1}+\mathbf {M}_2\\\mathbf {B}^*\mathbf {M}_1 & = 0\\\mbox{and} \quad \quad (\mathbf {S}-\mathbf {B}^*)\mathbf {M}_2 & = 0\) 
